Self-Similar Solutions in the Theory of Nonstationary Radiative Transfer in Spectral Lines in Plasmas and Gases

Symmetry

AlexanderV. Sokolov¹  VladimirV. Voloshinov¹  AndreiA. Kulichenko²  AlexanderB. Kukushkin²  PetrA. Sdvizhenskii²  VladislavS. Neverov² 

[1] Institute for Information Transmission Problems of Russian Academy of Sciences (Kharkevich Institute), 127051 Moscow, Russia;National Research Center “Kurchatov Institute”, 123182 Moscow, Russia;

关键词: radiative transfer;    superdiffusion;    Biberman–Holstein equation;    Lévy flight;    self-similar solution;   

DOI  :  10.3390/sym13030394

来源: DOAJ

【 摘 要 】

Radiative transfer (RT) in spectral lines in plasmas and gases under complete redistribution of the photon frequency in the emission-absorption act is known as a superdiffusion transport characterized by the irreducibility of the integral (in the space coordinates) equation for the atomic excitation density to a diffusion-type differential equation. The dominant role of distant rare flights (Lévy flights, introduced by Mandelbrot for trajectories generated by the Lévy stable distribution) is well known and is used to construct approximate analytic solutions in the theory of stationary RT (the escape probability method is the best example). In the theory of nonstationary RT, progress based on similar principles has been made recently. This includes approximate self-similar solutions for the Green’s function (i) at an infinite velocity of carriers (no retardation effects) to cover the Biberman–Holstein equation for various spectral line shapes; (ii) for a finite fixed velocity of carriers to cover a wide class of superdiffusion equations dominated by Lévy walks with rests; (iii) verification of the accuracy of above solutions by comparison with direct numerical solutions obtained using distributed computing. The article provides an overview of the above results with an emphasis on the role of distant rare flights in the discovery of nonstationary self-similar solutions.

【 授权许可】

Unknown